Jacobi functions and Euler products for Hermitian modular forms

One defines different types of Hecke operators on the spaces of Jacobi modular forms. For modular forms of genus two it is established that non-standard zeta-function $Z_p^{(2)}(s)$ with degree six of local factors is equal to the Dirichlet series constructed from the Fourier-Jacobi coefficients of eigeafunctions $F$. It is proved that $Z_p^{(2)}(s)$ can be continued analytically into the entire complex plane.